How to use an animation for one object on another object?
When you keyframed the locations on an object, an action has already been created


Select the object which should be animated
Switch to the Dopesheet and change to the Action Editor
Assign the action to your object. (default name here is Textaction) 


Note that the keyframes have absolute coordinates, I you're looking for relative changes you would need to offset them in the NLA-Editor (or alternatively change the origin of the individual text objects).

When you want start animations at different time offsets you would need to place them as Action-Strips in the NLA-Editor there you can move the strips to the time offset they should start (and even scale the duration).